This paper presents a computational study of free convection boundary-layer flow of non-Newtonian nanofluids over a vertical flat plate subjected to either constant wall temperature or constant wall heat flux, using a homogeneous flow model. The base fluid was an aqueous solution of 0.4 wt % carboxymethyl cellulose. The nanoparticles were: Al₂O₃, TiO₂, Cu and Au. The power-law model of viscosity was used for the base fluid. The coupled continuity, x-momentum and energy equations were solved simultaneously by pure implicit finite-difference technique. The parameters varied were: nanoparticle volume fraction (0-4%), nanoparticle diameter (25-100 nm), mean film temperature (30°-66°C) and wall heat flux (1-5.5 kW/m²). The theoretical models of Maxwell (for thermal conductivity) and Brinkman (for viscosity) predicted an almost linear increase in enhancement in heat transfer coefficient with increasing volume fraction of nanoparticles. On the contrary, use of the experimental property correlations of Corcione [11] showed a maximum enhancement for a particular volume fraction of nanoparticles. A set of correlations had been developed for calculating this optimum volume fraction for the four nanoparticle materials. Corcione models predicted higher enhancement with decreasing nanoparticle diameter and increasing mean film temperature or wall heat flux. Copper-carboxymethyl cellulose/Water and Gold-carboxymethyl cellulose/Water nanofluids were superior to Alumina-carboxymethyl cellulose/Water and Titania-carboxymethyl cellulose/Water in terms of enhancement in heat transfer coefficient. However, the largest enhancement was about 5.5%.